On the Lamb vector and the hydrodynamic charge
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This work is an attempt to test the concept of the hydrodynamic charge (analogous to the electric charge in electromagnetism) in the simple case of a coherent structure such as the Burgers vortex. We provide experimental measurements of both the so-called Lamb vector and its divergence (the charge) by two-dimensional particles images velocimetry. In addition, we perform a Helmholtz–Hodge decomposition of the Lamb vector in order to explore its topological features. We compare the charge with the well-known Q-criterion in order to assess its interest in detecting and characterizing coherent structure. Usefulness of this concept in studies of vortex dynamics is demonstrated.
KeywordsVortex Vorticity Particle Image Velocimetry Coherent Structure Vortex Core
Two of us (Sh. S. and V. S.) are grateful to E. Segre for providing us a multi-pass correlation algorithm and for his help in software support. This work is partially supported by grants from Israel Science Foundation, Binational US–Israel Foundation, and by the Minerva Centre for Nonlinear Physics of Complex Systems. G.R. was financially supported by a grant “post-doc CNRS” (S.P.M. section 02) during his post-doctoral stay in Nice. A.W. was supported by DFG grant SCHE 663/3-7.
- Clerk Maxwell J (1873) A treatise on electricity and magnetism. Clarendon PressGoogle Scholar
- Kirby RM, Marmanis H, Laidlaw DH (1999) Visualizing multivalued data from 2d incompressible flows using concepts from painting”. Proceedings of IEEE visualization 1999, San Francisco, CAGoogle Scholar
- Kollmann W, Umont G (2004) Lamb vector properties of swirling jets. Fifteenth Australasian fluid mechanics conference, Sydney, Australia, pp 13–17 available from http://www.aeromech.usyd.edu.au/15afmc/proceedings/papers/AFMC00081.pdf
- Lamb H (1878) On the conditions for steady motion of a fluid. Proc Lond Math Soc 9:91Google Scholar
- Polthier K, Preuß E (2003) Identifying vector field singularities using a discrete hodge decomposition. In: Hege H-C, Polthier K (eds) Visualization and mathematics III. Spinger, Berlin Heidelberg New YorkGoogle Scholar
- Saffman PG (1992) Vortex dynamics, Cambridge University PressGoogle Scholar
- Speziale CG (1989) On helicity fluctuations and the energy cascade in turbulence. In: Koh SL, Speziale CG (eds) Recent advances in engineering science. Lecture notes in Engineering, pp 39–10Google Scholar
- Tong Y, Lombeyda S, Hirani AN, Desbrun M (2003) Discrete multiscale vector field decomposition. SIGGRAPH 2003 Proceedings, ACMGoogle Scholar
- Wu J-Z, Ma HY, Zhou MD (2005) Vorticity and vortex dynamics. Springer, Berlin Heidelberg New YorkGoogle Scholar